A rigid-flexible coupled dynamic model of the planetary gear transmission system was developed considering the flexibility of the internal ring gear (flexible internal ring gear) and the sun shaft based on the shell theory and Timoshenko beam theory, respectively. For the dynamic modeling, the time-varying meshing stiffness and static transmission error excitations were considered and the Runge–Kutta numerical algorithm was applied to calculate the dynamic response. The results indicate that the flexibility of internal ring gear sharply decreases the dynamic factor between the internal ring gear and the planet gear, and it also shows significant positive influences on the system load-sharing performance. For the fixed internal ring gear, the maximum stress is located on the midpoint along the axial direction. The maximum dynamic deformations appear at the ends of the tooth surface along width direction, and the dynamic deformation shows a decremental trend from the tooth top edge to the tooth root edge. The load-sharing coefficient decreases rapidly with the increase in the thickness, as the support stiffness is small. The misalignment of one of the planet pins and various static transmission errors have a negative influence on the load-sharing coefficient of the planetary gear transmission system.

中文翻译：

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考虑内齿圈柔性的行星齿轮传动系统动力学分析

分别基于壳理论和铁木辛柯梁理论，建立了考虑内齿圈（柔性内齿圈）和太阳轴柔韧性的行星齿轮传动系统刚柔耦合动力学模型。对于动态建模，考虑了时变啮合刚度和静态传输误差激励，并应用 Runge-Kutta 数值算法来计算动态响应。结果表明，内齿圈的柔度使内齿圈与行星轮之间的动态系数急剧降低，对系统均载性能也显示出显着的正向影响。对于固定内齿圈，最大应力位于沿轴向的中点。最大的动态变形出现在沿宽度方向的齿面端部，动态变形从齿顶缘到齿根缘呈递减趋势。由于支撑刚度较小，负载分担系数随着厚度的增加而迅速降低。其中一个行星销的错位和各种静态传动误差对行星齿轮传动系统的负载分担系数有负面影响。